The ideal gas monitor will measure impurities in a supply gas stream accurately, with high precision and high reliability. However, real gas analyzers have accuracy and precision which are limited by ambient temperature, barometric pressure, gas pressure and other conditions that necessitate frequent calibration. For example, the temperature of the environment, e.g., room, which houses the analyzer has a large effect on the reading of most standard analyzers. Variations of as little as 5.degree. F., such as between day and night, necessitate that the analyzer be calibrated at both temperatures in order to assure consistent results. Further, calibration requires that the analyzer be taken off line, disabling process measurements during the period of calibration. Of course, the frequency of calibrations also depends on the drift of the instrument and the sensitivity of the instrument to environmental changes. Likewise, barometric pressure, back pressure, and other conditions must be compensated in order to obtain reliable, consistent and accurate readings.
Some temperature induced variations, such as amplifier gain, may be easily compensated or eliminated to an insignificant level, using standard methods. Other variations, such as analyzer cell output, which are interactively affected by temperature and other factors, are not easy to compensate or eliminate.
The back pressure of the gas being sensed causes variation in analyzer cell output, in a manner not necessarily directly related to the partial pressure of the sensed species in the gas stream. This is due, for example, to a nonlinear response of the cell to increasing overall pressures. The standard method for compensating for back pressure is to employ a high cost process grade pressure sensor to accurately read the back pressure, allowing a correction without first separately compensating the transducer. Less accurate pressure sensors generally have limited applicability because of the importance of pressure compensation.
Present systems seek to compensate for or minimize temperature induced variation of the electronics by, for example, employing resistors, capacitors, and amplifier circuits which have low temperature coefficients, are temperature compensated or used in matched circuits. Resistors and capacitors, as well as other devices may be selected so that the temperature induced variations tend to be nulled or near linear under the conditions of interest.
The sensor cell of the analyzer, which is an electrochemical device, tends to be sensitive to many different factors, in addition to the gas being measured. The underlying chemical reaction may be non-linearly affected by temperature, and therefore the output will also vary non-linearly. For example, the chemical reaction kinetics may speed or slow with temperature, while diffusion, bulk transfer, or other factors may also be altered in a complex manner to alter the reaction or output.
The sensor may employ a liquid or a solid electrolyte. In general, electrolyte electrochemical sensors operate at higher temperatures to increase the mobility of the chemical species and conductance, and are therefore may be more sensitive to changes in temperature.
The causes of error in electrochemical gas analyzers are not well characterized. Therefore, while it is known that environmental variations do result in output variations, and that controlling these environmental variations may reduce the output variations, systems are not available which directly and adequately compensate the output for environmental variations. Thus, since a definitive model is not available, output compensation is not generally employed in high quality instruments, and rather error minimization through the use of environmental control and high quality compensating sensors is the approach taught by the art. Frequent calibration of "zero" and "span" is conducted to ensure accurate results. The use of gas analyzers tends to be mission critical and therefore fault intolerant and require high sensitivity, precision and accuracy.
Often, in order to eliminate the affects of temperature variation on the gas analyzer, the cell is placed in a constant temperature oven, which thermostatically regulates the operating temperature. This oven adds cost and bulk to the analyzer device, and increases the power consumption. The oven also does nothing to compensate for atmospheric pressure or back pressure, which are generally noncompensable according to the standard scheme, and which would in any case require the addition of expensive additional transducers and additional device complexity. Of note is that it would be extremely difficult to regulate the ambient pressure of the device, and the in-line process control usage of the device makes it difficult to control the back pressure. Thus, while temperature may be regulated, other factors still vary.
In an effort to reduce the cost of thermostatic ovens, low cost temperature sensors and switches may be employed, often resulting in less than optimal temperature control, and the need to calibrate the analyzer frequently.
Often, in order to electronically compensate the analyzer, devices are placed at critical locations. For example, a thermistor or thermocouple mounted in close proximity to or inside the cell senses the temperature at or in the cell. A thermistor has a resistance which varies with temperature, and may be used as a sensor in an electronic circuit that compensates the cell output. A thermistor is used because its nonlinear response to temperature may be used in a simple circuit to temperature compensate the sensor, and the electrochemical sensor and thermistor may be provided together as a replaceable, mostly interchangeable, unit. Therefore, a thermistor may be individually selected for each sensor, sensor lot or sensor type, to retain plug compatibility.
Therefore, because the analyzer output has a non-linear interdependence on sensed species, ambient temperature, back pressure, and other factors, adjustment for each independent factor by an independent adjustment leads to imperfect compensation. Further, the compensating devices themselves may have their own external dependencies which must also be compensated. For example, pressure transducers may be affected by ambient temperature. Further, due to the variety of sensors, reproducability from device to device will require individual, expensive calibration. Since the compensating device interactions may be non-linear, the compensating adjustments become extremely difficult and costly. In other words, high quality, high cost, internally compensated and linearized sensors may be employed, or a complex external compensation system must be employed. The art presently teaches against a unified compensation system due to its perceived cost and complexity, with the requirement that replaceable sensor components be interchangeable. The error budget of the apparatus is therefore apportioned between the individually compensated elements of the system, and high accuracy and precision sensors are employed which individually meet the requirements.
Neural networks are known processing systems for determining the solution to problems which are very difficult to handle by means of conventional logic systems. However, neural networks may be very difficult to validate or analyze, and therefore their use in "mission critical" applications may require extensive testing. Therefore, while conventional methods require complex algorithms, which explicitly formulate the relationship between input variables, neural nets "learn" the relationship between the variables. Neural networks may also require specialized hardware for acceptable performance, while the complex formulae of standard methods may be implemented with standard computing architectures. See, "VLSI Architectures for Neural Networks", IEEE MICRO, Dec. 31, 1989, pp 8-27, incorporated herein by reference.
U.S. Pat. No. 5,121,443 relates to a neural net system for analyzing chromatographic peaks. This reference discloses a system for characterizing a peak superimposed on a baseline.
U.S. Pat. No. 5,203,984, incorporated herein by reference, relates to a water quality monitoring system having an electrochemical cell which includes a neural network to improve precision. The water quality monitoring system of U.S. Pat. No. 5,203,984, however, does not disclose the use of a neural network to compensate a sensor for environmental variations, but rather to help process data from multiple chemical species-specific sensors to determine concentrations of the multiple species.
An artificial neural network (hereinafter "neural network") is a network of many processing elements ("units"), which may be implemented as parallel hardware or sequential processing on common hardware. The units are generally connected by unidirectional communication channels ("connections"), which carry numeric (as opposed to symbolic) data. The units operate on their local data and on the inputs they receive via the connections. Neural networks normally have great potential for parallelism, since the computations of the components are independent of each other. A neural network may therefore be either an algorithm, or actual hardware, whose design was motivated by the design and functioning of human brains and components thereof. See. FAQ in comp.ai.neural-nets, monthly posting, 28 Jan. 1995, incorporated herein by reference.
In a common type of neural net, the neural net includes input units, internal units (hidden layer) and output units. The input units are a first layer of the neural net. The internal units may be configured in one or more layers and the output units are the final layer in the net. Each of the input units supplies a signal to each of the internal units in the layer of the net adjacent to the input units. If the neural net has more than one layer of internal units, each unit in the first layer of internal units, i.e., the internal units receiving signals from the input units, generates an output signal that is provided to each internal unit in the second layer of internal units. Other layers of internal units are connected to adjacent layers of internal units in a similar manner. Each internal unit in the layer of internal units adjacent to the layer of output units provides a signal to each output unit. Each output unit provides an output signal.
For each neural net, the connections and/or weighting of connections must be provided so that for a given input pattern the neural net generates an appropriate output pattern. See, D. E. Rumelhart et al., "Learning Internal Representations by Error Propagation", in D. E. Rumelhart & J. L. McClelland (Eds.), Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Vol. 1), pp. 318-362, MIT Press, 1986, Cambridge, Mass. See also, U.S. Pat. No. 5,253,329, incorporated herein by reference.
Most neural networks have some sort of "training", whereby the weights of connections are adjusted, using a form of feedback, on the basis of presented patterns and desired results. In other words, neural networks "learn" from examples, just like children learn to recognize dogs from examples of dogs, and exhibit some structural capability for generalization. Neural networks normally have great potential for parallelism in implementation, since the computations of the components are generally substantially independent of each other.
In theory, neural networks can be designed to compute any computable function, i.e. they can do everything a normal digital computer can do. In particular, anything that can be represented as a mapping between vector spaces can be approximated to arbitrary precision by feedforward artificial neural networks, a common type.
In practice, neural networks are especially useful for mapping problems which are tolerant of some errors, have a substantial amount of example data available, but to which hard and fast rules can not easily be applied. Neural networks are, at least today, difficult to apply successfully to problems that concern manipulation of symbols and memory. Where accuracy and complete characterization are desired, neural networks may also be difficult to apply.
Backpropagation of error, or "backprop", is a commonly used training method for neural networks. Backpropagation of error allows the neural network weights to "automatically" adjust based on a feedback of an actual result as compared to a result predicted by the neural network from a set of inputs. Because a model is not employed in defining these weights, the network may sometimes display artifacts or aberrant responses for input conditions which differ from training data, or model too closely the training data without regard for the true importance of any differences between an actual input condition and a training condition. Those skilled in the art therefore employ known techniques to optimize the training procedure.
Backpropagation of errors is often used for the training of layered (i.e., nodes are grouped in layers) feedforward (i.e., the data connection joining nodes are unidirectional, and there are no cycles) nets, often called "multilayer perceptrons".
Backpropagation of errors generally requires a "teacher" that knows the correct output for any input set ("supervised learning") and uses gradient descent on the error (as provided by the teacher) to train the weights. The activation function is (usually) a sigmoidal (i.e., bounded above and below, but differentiable) function of a weighted sum of the nodal inputs. The use of a gradient descent algorithm to train its weights makes it slow to train; but being a feedforward algorithm, it is quite rapid during the recall phase. Other types of training are also known.
"Overfitting" (often also called "overtraining" or "overlearning") is the phenomenon wherein the accuracy of the input/output relationship developed by the network decreases after a certain optimal point during training. This phenomenon arises because such long training causes the network to "memorize" the training patterns, including all of their peculiarities, whereas one is usually interested in the generalization of the network; i.e., the error it exhibits on examples not seen during training. Learning the peculiarities of the training set may therefore reduce the generalization capability of the neural network. The network should only be allowed to learn the general structure of the examples.
There are various methods used to fight overfitting. The two most important classes of such methods are regularization methods (such as weight decay) and early stopping. Regularization methods try to limit the complexity of the network such that it is unable to learn peculiarities. Early stopping aims at stopping the training at the point of optimal generalization. This latter method is typically achieved through the use of a pattern "test set". The original group of input patterns randomly split into two groups: the training set and the test set. While the training patterns drive the network weight changes, the test patterns are used only to monitor network performance. For a given iteration, the entire set of training patterns are presented to the network and the weights are adjusted accordingly. Next, the error over the test pattern set is calculated. The error for the training set will usually decrease with increasing iterations. The error for the test set, on the other hand, will typically reach a minimum when the generalization capabilities of the network are strongest. Beyond this point, the test set error increases, signifying that the network is overfitting the training patterns at the expense of learning the general relationship.